Responding to Objections 4: Axioms

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• published: 27 Jan 2014
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UPDATE: After finally studying a decent, formal reference in propositional logic, I can now confidently say that this video is shit. But I'm going to leave it up anyway for learning purposes, because it shows a fun stage of development in my study of epistemology. The biggest error in this video is my abuse of the word "axiom." An axiom is a proposition that we arbitrarily map to a value of "true." The correct term I was looking for was actually "truth assignment function." This is the operator that maps propositions to truth values. Another useful concept is the "rule of inference," which simply generates new true propositions out of old ones. This is a major part of propositional logic. Mental incorrigibility is a truth assignment that I find very useful. Definitional propositions seem to fall in this category as well. Axiomatic systems for mathematics and logic also serve as viable truth assignments when understood for what they are. Finally, the pragmatic maxim serves as the ultimate arbiter of truth when building viable models for objective reality. ------------------------------------------------ A discussion on the epistemic nature of axioms; where they come from, how we use them, and how people tend to misunderstand their purpose. Axioms of analytic propositions: 1) All consistent axioms are TRUE. 2) All incorrigible propositions are TRUE. *Corollary: All assignment declarations are TRUE. 3) All assignment declarations are transitive. 4) All incoherent propositions are FALSE. 5) All epistemic evaluations are TRUE. Axiom of synthetic propositions: 6) For every synthetic propositions P, there exists an action A and consequence C. If P is TRUE, then doing A will achieve C. If doing A fails to achieve C, then P is FALSE. UPDATE: It's been pointed out that Axiom #4 is not consistent with the law of negation. This is a good point. Two possible fixes may include 1) Redefine negation to only operate on coherent propositions. 2) Define an alternative, third category of epistemology. Call them TRUE, FALSE, and INCOHERENT. Incoherent propositions are therefore neither true nor false. Either of these fixes seem to address the issue to me. What do you think is more elegant and functional?